| With the rapid development of data acquisition technology, people obtain more and more comprehensive data in the field of bioinformatics, medicine and health care, and data dimension is higher and higher, the application of traditional model selection method is restricted. Nowadays high-dimensional data analysis and modeling is one of the hotspot in field of statistics, how to reduce the dimension is a major challenge for high- dimensional data analysis.Traditional cox proportional hazards regression model is a most commonly used method for survival data analysis, but it no longer apply to high dimension data. Variable selection is an effective way to deal with these high-dimensional data, while SCAD and ADS are typical ones. In this thesis we promote SCAD and ADS methods of the linear model to the proportional hazards model and study their characterization, main research are as follows:(1)In this thesis we define SCAD method in the COX model, construct β estimator of SCAD punishment function, discusses large sample result of SCAD method for high dimensional survival data analysis, show that SCAD possesses an oracle property. We propose the SCAD variable selection method, which improves the LASSO, the SCAD reserves big parameters of the initial model and compress those variables which are not significant to 0, effectively reduce the deviation of the model. Simulation study show that SCAD variable method is more effective in computation than the LASSO. Finally, we carry on the instance to test the superiority of the SCAD method.(2) In this thesis we define ADS method in the COX model, show that ADS possesses an oracle property, theoretically prove that the ADS method can realize the variable selection and parameter estimation in COX model. Base on the data of common variable dimension is greater than the sample size, propose the ADS variable selection method, simulation study show that ADS variable method is more effective in computation than the LASSO and DS method. |
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